Whenever you take a flash photo, you're basically combining two exposures together in one shot: the flash exposure made with light from the flash, and ambient exposure, made with all the light that's not from the flash. And the controls for those two types of exposure are different.
Ambient exposure is controlled by iso, aperture, and shutter speed.
Is this a conscious decision that manufacturers have made not to include such feature, so that photographers can be aware of the HSS flash power limitations?
In my opinion, yes, I think this is why it's usually implemented the other way around: that you have to turn HSS on, and then the camera only stops using HSS if the shutter speed falls below sync speed....
The flash settings might not be the problem.
In full sun, ISO 200, 1/200th second at f5.0 is about three stops over-exposed.
High speed sync along with a faster shutter speed might produce the results you want. Likewise neutral density filters are another alternative.
Nikon speedlights automatically switch into HSS, and Godox strobes do as well with the correct TTL radio trigger. You just have to set the flash sync to 1/250* (or 1/320*) in the camera's menu. The star indicates "auto FP" which is focal plane shutter sync (HSS in Nikon language).
I'm pretty sure others do/can as well.
But there is ...
A high-speed sync mode is in certain manner equivalent to using a neutral density filter.
If you use ND4 filter, you get one fourth of the light through the filter in front of the lens. This reduces all aspects of exposure, both flash exposure and ambient exposure to one fourth of what they used to be.
If you use high-speed sync with a 4 times ...